Matlab傅立叶描述符有什么问题? [英] Matlab fourier descriptors what's wrong?

问题描述

我正在使用Gonzalez frdescp函数来获取边界的傅立叶描述符.我使用这段代码，得到了两个完全不同的数字集，描述了两个相同但尺度不同的数字.

I am using Gonzalez frdescp function to get Fourier descriptors of a boundary. I use this code, and I get two totally different sets of numbers describing two identical but different in scale shapes.

那怎么了?

im = imread('c:\classes\a1.png');
im = im2bw(im);
b = bwboundaries(im);
f = frdescp(b{1}); // fourier descriptors for the boundary of the first object ( my   pic only contains one object anyway )
// Normalization
f = f(2:20); // getting the first 20 & deleting the dc component
f = abs(f) ;
f = f/f(1);

为什么我对于两个相同的圆圈却得到了不同的描述词-但是在比例上却不同?

Why do I get different descriptors for identical - but different in scale - two circles?

推荐答案

问题是frdescp代码(我使用了

The problem is that the frdescp code (I used this code, that should be the same as referred by you) is written also in order to center the Fourier descriptors.

如果要以正确的方式描述形状，则必须保留一些相对于表示DC分量对称的描述符.

If you want to describe your shape in a correct way, it is mandatory to mantain some descriptors that are symmetric with respect to the one representing the DC component.

下图概述了概念:

为了解决您的问题(以及其他类似的问题)，我编写了以下两个函数:

In order to solve your problem (and others like yours), I wrote the following two functions:

function descriptors = fourierdescriptor( boundary )
    %I assume that the boundary is a N x 2 matrix
    %Also, N must be an even number

    np = size(boundary, 1);

    s = boundary(:, 1) + i*boundary(:, 2);

    descriptors = fft(s);

    descriptors = [descriptors((1+(np/2)):end); descriptors(1:np/2)];
end

function significativedescriptors = getsignificativedescriptors( alldescriptors, num )
    %num is the number of significative descriptors (in your example, is was 20)
    %In the following, I assume that num and size(alldescriptors,1) are even numbers

    dim = size(alldescriptors, 1);

    if num >= dim
        significativedescriptors = alldescriptors;
    else
        a = (dim/2 - num/2) + 1;
        b = dim/2 + num/2;

        significativedescriptors = alldescriptors(a : b);
    end
end

知道，您可以按以下方式使用上述功能:

Know, you can use the above functions as follows:

im = imread('test.jpg');
im = im2bw(im);
b = bwboundaries(im);
b = b{1};

%force the number of boundary points to be even
if mod(size(b,1), 2) ~= 0
    b = [b; b(end, :)];
end

%define the number of significative descriptors I want to extract (it must be even)
numdescr = 20;

%Now, you can extract all fourier descriptors...
f = fourierdescriptor(b);
%...and get only the most significative:
f_sign = getsignificativedescriptors(f, numdescr);

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